Reflection, Refraction and Polarization of EM wave · Law of reflection Law of refraction. 30 May...

$: Reflection, Refraction and Polarization of EM wave · Law of reflection Law of refraction. 30 May 2020 PPN College, Kanpur 7 Fresnel Equation for Reflection and Refraction of EM wave$
Reflection, Refraction and Polarization of EM wave

PPN College, Kanpur

Department of Physics, P. P. N. (PG) College,

Kanpur – 208 001, U.P., IndiaEmail: [email protected],

[email protected]: dkpandey.weebly.com

Dharmendra Kumar Pandey

30 May 2020 1

mailto:[email protected]

30 May 2020 PPN College, Kanpur 2

Boundary condition for EM wave

1. The normal component of electricdisplacement vector is not continuous atthe interface but changes by an amountequal to the free surface charge density.

2. The normal component of magneticinduction B is continuous across theinterface.

D-D 2n1n

0B-B 2n1n

D K P

ande

y, PPN C

olleg

e, Kan

pur

30 May 2020 PPN College, Kanpur 330 May 2020 PPN College, Kanpur 3

Boundary condition for EM wave

3. The tangential component of electric field iscontinuous at the interface.

4. The tangential component of magnetic fieldstrength is not continuous at the interfacebut changes by an amount equal to thecomponent of the surface current densityperpendicular to tangential component of H.

0E-E 2t1t

JH-H S2t1t

D K P

ande

y, PPN C

olleg

e, Kan

pur


Reflection and Refraction of EM waveFor Incident wave

)tr.1K(i

011 eEE

1

111

EKB

11

111

EKH

For reflected wave)tr.1K(i

011 eEE

1

111

EKB

11

111

EKH

)tr.2K(i

022 eEE

2

222

EKB

11

111

EKH

For refracted wave

D K P

ande

y, PPN C

olleg

e, Kan

pur

30 May 2020 PPN College, Kanpur 530 May 2020 PPN College, Kanpur 5

Reflection and Refraction of EM wave

Since, tangential component of electric field iscontinuous at interface .

t2t1t1 )E()E()E(

)t2r.2k(i

t02

)t1r.1k(i

t1o

)t1r.1k(i

t01 e)E(e)E(e)E(

211

)r.2k(i

t02

)r.1k(i

t1o

)r.1k(i

t01 e)E(e)E(e)E(

t02t1ot01 )E()E()E(for ,Therefore

0z20z10z1 )r.k()r.k()r.k(

D K P

ande

y, PPN C

olleg

e, Kan

pur

30 May 2020 PPN College, Kanpur 630 May 2020 PPN College, Kanpur 630 May 2020 PPN College, Kanpur 6

Reflection and Refraction of EM wave

11 kk

r1i1 sinxksinxk

0z10z1 )r.k()r.k( ,If

Since wave propagationvector does not vary insame medium thus

ri sinsin

ri

0z20z1 )r.k()r.k( ,If

r2i1 sinxksinxk

1

2

r

i

k

k

sin

sin

2

1

1

2

r

i

v

v

k

k

sin

sin

11

22

2

1

r

i

v

v

sin

sinn

Law of reflection Law of refractionD K

Pan

dey,

PPN Coll

ege,

Kanpu

r


Fresnel Equation for Reflection and Refraction of EM wave

A: When E is perpendicular to plane of incidence

r

2

2i

1

1

r

2

2i

1

1

01

01

coscos

coscos

E

E

r

2

2i

1

1

i

1

1

01

02

coscos

cos2

E

E

D K P

ande

y, PPN C

olleg

e, Kan

pur


)sin(

sincos2

cosncosn

cosn2

E

E

ri

ri

r2i1

i1

01

02

Fresnel Equation…………. contdfor Reflection and Refraction of EM wave

r

i

1

2

1

2021

sin

sin

n

n then if

)sin(

)sin(

cosncosn

cosncosn

E

E

ri

ri

r2i1

r2i1

01

01

For normal incidence ; i=r=0

21

21

01

01

nn

nn

E

E

21

1

01

02

nn

n2

E

E

D K P

ande

y, PPN C

olleg

e, Kan

pur


Case 1: when (n1/n2)<1 ; wave : rare to densern=Sini / Sinr =(n2/n1)>1 and i > r


2differencePath ; Change Phase ve

E

E

01

01

Reflected and incident wave are in opposite phase.Refracted and incident wave are in same phase.

Case 2: when (n1/n2)>1 ; wave :denser to raren=Sini / Sinr =(n2/n1)<1 and i < r

0 Change Phase veE

E

01

01

Reflected and incident wave are in same phase.Refracted and incident wave are in same phase.

0 Change Phase veE

E

01

02

0 Change Phase veE

E

01

02

D K P

ande

y, PPN C

olleg

e, Kan

pur



B: When E is parallel to plane of incidence

r

1

1i

2

2

r

1

1i

2

2

01

01

coscos

coscos

E

E

r

1

1i

2

2

i

1

1

01

02

coscos

cos2

E

E

D K P

ande

y, PPN C

olleg

e, Kan

pur


)cos()sin(

sincos2

cosncosn

cosn2

E

E

riri

ri

r1i2

i1

01

02

r

i

1

2

1

2021

sin

sin

n

n then if

)tan(

)tan(

cosncosn

cosncosn

E

E

ri

ri

r1i2

r1i2

01

01


12

12

01

01

nn

nn

E

E

12

1

01

02

nn

n2

E

E


D K P

ande

y, PPN C

olleg

e, Kan

pur


Fresnel Equation…………. Contd….for Reflection and Refraction of EM wave

Case 1:

Refracted and incident wave are in same phase.

0 Change Phase veE

E

01

02

Case 2: From both cases we found that -

)tan(

)tan(

E

Er

ri

ri

II01

01II

)sin(

)sin(

E

Er ;

ri

ri

01

01

1

21

riBprin

ntan

2 or

2 if

0r and 0rII Thus , if an un-polarized light incidents (rare to denser) at angle p= B thenonly electric vector perpendicular to plane of incidence will be reflected andlight will become polarized. This angle is termed as angle of polarization orBrewster’s angle.D K

Pan

dey,

PPN Coll

ege,

Kanpu

r


Fresnel Equation…………. Contd….for Reflection and Refraction of EM wave

Case 3: if em wave travels from denser to rarer medium then it goes away from normal.

)tan(

)tan(

E

Er

ri

ri

II01

01II

)sin(

)sin(

E

Er ;

ri

ri

01

01

1

21

cirn

nsinor

2

1r and 1rII

1rR and 1rR22

IIII

Thus total energy is reflected at the interface of two mediums.This means, as the angle of incident wave increases, the intensity ofreflected wave increases while intensity of refracted wave diminishes. Theintensity of refracted wave becomes zero at i=c. But if i>c then wavecompletely goes in medium Ist, and follows law of reflection. This is TIR.

D K P

ande

y, PPN C

olleg

e, Kan

pur


Reflection and transmission coefficient

2

01

2

01

2

011

2

011

)E(

)E(

)E(v

)E(v

aveincident w ofIntensity

wavereflected of IntensityR

2

012

2

021

2

011

2

022

)E(k

)E(k

)E(v

)E(v

aveincident w ofIntensity

waveed transmittof IntensityT

2

011

2

022

)E(n

)E(nT


12

12

01

01

nn

nn

E

E

12

1

01

02

nn

n2

E

E

1TR

Note : Degree of polarization

)(tan

)(tanR &

)(sin

)(sinR ;

RR

RRP

ri

2

ri

2

II

ri

2

ri

2

II

II

D K P

ande

y, PPN C

olleg

e, Kan

pur


Faraday Effect or Faraday Rotation

When an isotropic medium of high refractive index isplaced in strong magnetic field, then it becomesoptically active temporarily.

If a plane polarized EM wave passes through suchmedium then its plane of polarization is rotated. This iscalled as Faraday rotation.

BL

VBL

V=Verdet constant

V

1mL and 1TB ,If

D K P

ande

y, PPN C

olleg

e, Kan

pur

PPN College, Kanpur

A Lot of Thanksfor attention

30 May 2020 16

Reflection, Refraction and Polarization of EM wave · Law of reflection Law of refraction. 30 May...

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